Examples Performing a Hypothesis Test
In the spring of 2006, all students registered for STAT200 were asked to complete a
survey. A total of 1004 students responded. If we assume that this sample represents the
PSU-UP undergraduate population, then we can make inferences regarding this
population based on the survey results.
Question: Would you date someone with a great personality even if you did not find them
attractive?
1. What would be the correct hypothesis to determine if there is a difference in gender between
the true percentages that would date someone with a great personality even if they did not find
them attractive among PSU-UP undergraduate students?
Ho: p1 – p2 = 0 and Ha: p1 – p2 ≠ 0
Test and CI for Two Proportions: DatePerly, Gender
Event = Yes
Gender
female
male
X
367
148
N
571
433
Sample p
0.642732
0.341801
Difference = p (female) - p (male)
Estimate for difference: 0.300931
95% CI for difference: (0.241427, 0.360435)
Test for difference = 0 (vs not = 0)
Z = 9.91 P-Value = 0.000
Conclusion and Decision: Since the p-value is less than 0.05 we would reject the null
hypothesis and conclude that there is statistical evidence that a difference exists between
the true proportion of female students who would date someone with a great personality
if not attracted to them and the true proportion of males who would do so.
Question: What are the measurements of the span of your right and left hand?
2. What would be the correct hypothesis to determine if mean right hand spans longer than mean
left hand spans among PSU-UP undergraduate students?
Ho: ud = 0 and Ha: ud > 0
Paired T-Test and CI: Rspan, Lspan
Paired T for Rspan - Lspan
Rspan
Lspan
Difference
N
922
922
922
Mean
20.6837
20.6355
0.048134
StDev
2.3194
2.3332
0.798840
SE Mean
0.0764
0.0768
0.026308
95% CI for mean difference: (-0.003497, 0.099766)
T-Test of mean difference = 0 (vs not = 0):
T-Value = 1.83 P-Value = 0.068
Conclusion and Decision: Since the p-value is less than 0.05 but is for a two-sided test
(note that minitab says “not = 0”), and thus with our Ha using > we need to divide this pvalue by 2. That results in a p-value of 0.034 meaning we would reject the null
hypothesis and conclude that there is statistical evidence that, on average, the true mean
length of right hand spans is greater than the true mean length of left hand spans for PSUUP undergrads.
Question: About how many days per month do you drink alcohol?
3. Some students who belong to Greek organizations believe that they do not drink anymore than
non-greek students. However, the university administration does not agree, and think that the
greek population drinks more often than their non-greek counterparts. What would be the correct
hypothesis to determine if the administration is correct? Assume that non-greeks are population
u1 and greeks are u2.
Ho: u1 – u2 = 0 and Ha: u1 – u2 < 0
Two-Sample T-Test and CI: DaysAlco, Greek?
Two-sample T for DaysAlco
Greek?
No
Yes
N
806
191
Mean
7.29
11.01
StDev
5.52
4.58
SE Mean
0.19
0.33
Difference = mu (No) - mu (Yes)
Estimate for difference: -3.71243
95% CI for difference: (-4.55847, -2.86639)
T-Test of difference = 0 (vs not =):
T-Value = -8.61 P-Value = 0.000 DF = 995
Both use Pooled StDev = 5.3574
Conclusion and Decision: Since the p-value is less than 0.05 but is for a two-sided test
(note that minitab says “not = 0”), and thus with our Ha using < we need to divide this pvalue by 2. This results in a p-value of approximately 0.00 meaning we would reject the
null hypothesis and conclude that there is statistical evidence that on average, the greek
population drinks more days per month than the non-greeks at PSU-UP.